Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The straight line y = 2x + λ does not meet the parabola y 2 = 2x, if
A
λ < 
B
λ > 
C
λ = 4
D
λ = 1
Text Solution
Verified by ExpertsThe correct answer is:
B
line y = 2x + λ …(i)
Parabola y 2 = 2x …(ii)
From (i) & (ii) (2x+ λ ) 2 = 2x
⇒ 4x 2 + 4x λ + λ 2 = 2x
⇒ 4x 2 + 2x(2 λ – 1) + λ 2 = 0
Does not meet the parabola D < 0
⇒ 4(2 λ – 1) 2 – 4(4)( λ 2 ) < 0
⇒ 4[4 λ 2 + 1 – 4 λ – 4 λ 2 ] < 0
⇒ 1 – 4 λ < 0 ⇒ λ > ¼
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